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Full text of "Mathematical And Physical Papers - Iii"

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variation of c would be small quantities of the second order, since c only appears multiplied by du/dt, and therefore c may be regarded as constant.
It remains to form the expressions for fx, fy, fz. By the conduction of heat we mean that sort of communication which takes place between the contiguous portions of bodies. In the case of bodies which are partially diathemwus, that is to say, which behave with respect to heat, or at least heat of certain degrees of refrangibility, in the same way in which semi-opaque bodies behave with respect to light, or rather in which a green glass behaves with respect to red rays, heat may be communicated from one portion of the body to another situated at a sensible distance. But this is, properly speaking, internal radiation, and not conduction. Again, if the solid be perfectly diather-mous to heat of certain degrees of refrangibility, a portion in the interior of the mass may by radiation send heat out of the solid altogether. For my own part I believe conduction to be quite distinct from internal radiation, although the theory which makes conduction to be nothing more than molecular radiation and absorption seems to be received by many philosophers with the most implicit reliance. No doubt internal radiation may, and I believe generally if not always does, accompany conduction: and when the distance which a ray of heat can travel before it is absorbed is insensible, we may include internal radiation in the mathematical theory of conduction, and even, if we please, in our definition of the word conduction. Of course the distance which we may regard as insensible will depend partly on the dimensions of the body, partly upon certain lengths relating to the state of temperature in the interior, and depending upon the problem with which we have to deal. As an example of a length of this sort, we may take the distance between consecutive maxima, if we are considering the internal temperature of a solid of which the surface has a temperature that is subject to periodic variations.
4. Let us now confine ourselves to conduction, using that term with the extensions and restrictions above explained. The temperature u is supposed to be sufficiently small to allow ns to superpose different systems of temperature without mutual disturbance. If the temperature were the same at all points, there